Question: Solve for $x$ and $y$ using elimination. $\begin{align*}x+2y &= 4 \\ 7x-2y &= -2\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $8x = 2$ Divide both sides by $8$ and reduce as necessary. $x = \dfrac{1}{4}$ Substitute $\dfrac{1}{4}$ for $x$ in the top equation. $ \dfrac{1}{4}+2y = 4$ $\dfrac{1}{4}+2y = 4$ $2y = \dfrac{15}{4}$ The solution is $\enspace x = \dfrac{1}{4}, \enspace y = \dfrac{15}{8}$.